The quantification of foreign particle transport, including heterogeneity in particle diffusion, is necessary for the development of effective transmucosal drug delivery methods, and more generally of particle penetration through biological structures and synthetic gels. Every organ, as well as the eyes, nasal tract and female reproductive tract, is protected by a layer of mucus. It is increasingly recognized that transmucosal delivery is a pathway for treating disease throughout the entire body. Pulmonary drug delivery is of particular interest because it has been shown to lead to a direct targeting of the drug carrier load to epithelial cells (e.g., for lung cancer) and immense lung vasculature, to a reduction in side effects, to faster drug onset times, and to controlled release times of drugs from carrier particles by tuning diffusion timescales relative to carrier particle drug release timescales. Inhalation has been identified as a potentially superior method of drug delivery for a range of conditions such as chronic obstructive pulmonary disease (COPD), asthma and cystic fibrosis, and lung cancer. Inhalation has also been proposed as a delivery mechanism for vaccines, gene therapies, and insulin.
Despite the benefits and wide range of potential applications, the results of clinical transmucosal-based treatments have been mixed for a variety of reasons, e.g., inconsistencies in understanding and measurement of drug uptake. A poor quantitative understanding of drug carrier particle transport in and through the mucus barrier is a key factor for these inconsistencies. Mucus concentration (determined by % solids including a spectrum of mucins, salts, and proteins, and a measure of airway liquid hydration) varies dramatically across organs but also between samples taken from the same organ. Within the gastrointestinal tract, for example, the thickness and physical properties of the mucus layer vary by location as well as diet. Mucus properties in the lung are similarly variable with mucus layer thickness ranging from a small fraction of a micron (μm) to 50 μm depending on location in the lung and many other factors (chronic cough, for example). Mucus concentration likewise varies with age, disease progression, and across populations. Diseases such as cystic fibrosis and COPD cause the physical properties of mucus to change dramatically during disease progression.
Due to this high variability, it has been difficult to accurately control drug residence time in the mucosal layer relative to the chemical degradation of the carrier particle and relative to the innate clearance time of the mucus layer. The key information about passage times through the mucosal layer to reach epithelial tissue and vasculature is poorly understood, and thereby typically not addressed in drug delivery estimates. This is further exacerbated by the fact that drug inhalation particles are often tested on animal models prior to clinical trials, adding further variability and making it difficult to interpret results. Several years ago, the need to quantify the differences in transmucosal drug penetration between parts of the body as well as diseased and healthy states was recognized, but progress has been slow due to the complexity of the required experiments and the lack of progress on rigorous analysis of experimental data.
Conventional approaches to modeling particle diffusion through mucus layers use observed data to determine the effective viscosity of a fluid, and infer an effective diffusion coefficient over the timescale of the experiment. The industry standard method for determining a particle's diffusivity in mucus involves calculating the mean squared displacement (MSD) and this value is often reported as a fraction of the diffusivity of that particle in water. In other words, there is an assumption that the MSD of a particle undergoing Brownian motion scales linearly with time, a behavior which is herein referred to as “normal” diffusion behavior. While this provides a useful benchmark for comparing diffusion rates versus particle size, shape and surface chemistry, it is a simplification with unquantifiable errors of the underlying complexity in the system. Determining the diffusivity from the pre-factor of the MSD assumes that the diffusion process can be described by a single diffusion coefficient, and that the MSD is linear in time.
Research has shown, however, that the MSD of a particle traveling through human lung mucus, for example, does not obey simple diffusion processes and does not scale linearly with time, but in fact scales more slowly than would be expected for normal diffusion, behavior which is herein referred to as “scaling sub-diffusively”. The data reveal that micron diameter particles in mucus exhibit sub-diffusive behavior, with a fractional power of lag time rather than scaling linearly in time. As a result, any model that is based on the assumption of normal diffusion of particle through human lung mucus will not accurately represent the behavior of real mucus. For normal diffusion, one can rigorously infer how passage time distributions scale with the thickness of the layer being penetrated; for sub-diffusive processes, there is no method known in the prior art to determine how passage times depend on layer thickness, and it therefore must be estimated by alternative methods presented below. This is problematic for medical treatments that use inaccurate diffusion models to calculate dosing, for example, especially since the complex viscosity of the mucus layer changes as the disease progresses or in response to treatment, and since layer thicknesses are variable within lung airways.
Another problem with conventional approaches to modeling particle diffusion through mucus layers is that the mucus is assumed to have a uniform characteristic throughout. That is, one can ascribe an average diffusivity and any predictions about particle transport will be accurately approximated on this basis. In reality, mucus layers may have channels through which particles quickly pass through the mucus layer to the underlying tissue and vasculature, and mucus layers may have pockets of highly contrasted physical properties, which tend to capture and sequester particles within the mucus layer. It is therefore critical to assess the likelihood of outlier particles that exhibit both the fastest and slowest passage times, and to quantitatively estimate those passage times. Clearly, since normal or simple diffusion processes do not accurately model sub-diffusion through homogeneous mucus and similar biomaterials, the situation is magnified in the presence of heterogeneity. Current predictions of passage times through mucosal layers, and their scaling with layer thickness, based on simple diffusion processes, are consequently highly inaccurate. As a result, any model that assumes that all similar particles travel through the mucus at the same normal diffusion rate will not accurately reflect the behavior of particles in real mucus, and in fact the errors made in such estimates are unquantifiable without an alternative, rigorously based, protocol. Such a protocol is the basis of this application.
These types of issues play a direct role in the inconsistencies between theoretical and experimental drug uptake. Because the current standard methods do not accurately describe how sub-micron to several micron diameter particles diffuse in mucus and other biofluids, biogels, blood clots, etc., it has been difficult to determine what percent of a drug will make it through the mucus barrier or related biological layer, and therefore difficult to determine what effective dose has reached the target relative to other timescales (mucus clearance, particle degradation). In order to better describe the drug uptake process, it is highly desirable to accurately determine the passage times of particles traversing the mucosal layer as a function of layer thickness.
Accordingly, in light of these disadvantages associated with conventional approaches for determining a particle's diffusivity in mucus, there exists a need for more accurate methods. More specifically, there is a need for methods, systems, and computer readable media for data analysis and inference of particle diffusion in mucus barriers.